Berlin 2015 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 27: Statistical Physics far from Thermal Equilibrium - Part I

DY 27.6: Vortrag

Mittwoch, 18. März 2015, 11:15–11:30, BH-N 334

Synchronization of moving oscillators — •Robert Großmann¹, Fernando Peruani², and Markus Bär¹ — ¹Physikalisch-Technische Bundesanstalt, Abbestraße 2-12, 10587 Berlin, Germany — ²Université Nice Sophia Antipolis, Laboratoire J.A. Dieudonné, UMR 7351 CNRS, Parc Valrose, F-06108 Nice Cedex 02, France

We consider an extension of the Kuramoto model of noisy phase oscillators with local interaction, where individual oscillators move randomly in D dimensional space. We study this model by using both analytical and numerical methods to answer the question how the synchronization is influenced by the motion of individual oscillators. Our model displays a non-equilibrium order-disorder transition from a desynchronized to a synchronized state depending on the noise acting on individual oscillators. The properties of the transition crucially depend on the spatial dimensionality and the diffusion-type of oscillators: We consider both normal diffusive motion as well as super-diffusively moving oscillators. We derive field equations which describe the large-scale dynamics of the system by means of Langevin equations for order parameters. By coarse-graining the model in this way, we are able to analyze the large-scale dynamics analytically. In particular, we study how fluctuations on the microscale (oscillator dynamics) enter the macroscopic dynamics (field theory) and calculate order-parameter correlation functions. Our theory suggests that a transition to long-range synchronization in D ≤ 2 is not possible, if individual oscillators move diffusively. In contrast, long-range synchronization is possible in any spatial dimension for certain types of superdiffusive motion.